TY - JOUR
T1 - An $hp$-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 969
EP - 994
PY - 2019
DA - 2019/04
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2018-0104
UR - https://global-sci.org/intro/article_detail/nmtma/13139.html
KW - Chebyshev spectral collocation method, nonlinear Volterra integro-differential equations, weakly singular kernels, error analysis.
AB - <p style="text-align: justify;">This paper presents an $hp$-version Chebyshev spectral collocation method for
nonlinear Volterra integro-differential equations with weakly singular kernels. The $hp$-version error bound of the collocation method under the $H$<sup>1</sup>-norm is established on an
arbitrary mesh. Numerical experiments demonstrate the effectiveness of the proposed
method.</p>